Lesson 3 — How Many Are There?

Summary

Learners deepen the idea of cardinality — that the last number spoken when counting a group is the answer to “how many there are.” They count several collections of different sizes, say the total for each, and check by counting again.

Objectives

• Count a group of objects and name the total number (“how many”). (D05.S1.K.01)

Connection

Whenever someone asks “how many?” they are asking you to count — the fish in the net, the eggs in the basket, the people at the table. The answer is the last number you say when you count, and then you can count again to be sure. Counting and checking is how people everywhere make sure nothing is lost and everyone gets their fair share.

Materials

• Several small collections of different sizes (3, 7, 12, 20 items), each in its own cup or pile
• A cloth or box for hiding a collection

Preparation

• Prepare 3-5 collections of different sizes per learner or pair (for example 3 shells, 7 beans, 12 pebbles, 20 leaves).
• Arrange them so each collection has a clear, separate spot.

Facilitator note

This lesson is written to the learner (“you”). The key idea is cardinality: the last counting word is the number of things in the set — a concept young children master at different times and must be allowed to arrive at gradually (Clements & Sarama, 2014). Some learners will touch-and-count perfectly and still answer “five” no matter how many there are; that is a normal step on the way, not a failure. When that happens, ask gently, “What was the last number you said?” rather than correcting. Never rank learners or praise only the fastest. Count in the home language. Learners who are blind or low-vision can count by moving objects one at a time into a cup and noticing the growing pile by feel; learners who are deaf or hard of hearing can sign the numbers. Learners with limited hand or body movement name totals by voice or sign while a partner moves each object, or indicate each object with eye-gaze or a mouth stick for a partner to move and count. The “how many?” game should feel like play, never like a test.

Procedure

1. Gather (5 min). Look at your collections. Some look big, some look small. You cannot always tell how many just by looking — you have to count.
2. Count and name (15 min). Pick one collection. Count it, touching each thing and saying one number for it. The last number you say is how many. Say it clearly: “There are seven.” Do this for each collection.
3. Count again to check (10 min). Count the same collection a second time. Does the last number match? Counting twice and getting the same answer is how you know your count is true.
4. The how-many game (10 min). With a friend, one of you hides a small pile under a cloth. The other peeks for only a blink, then must count carefully to say “how many.” Switch turns. No rushing — slow counting is good counting.
5. Close (5 min). Remember: the last number you say is your answer. Count once, then count again to check. That is how we know.

Differentiation

• Support: Use very small collections (1-4) and count hand over hand, pausing on the last object to say the total together.
• Extension: Invite learners to line up their collections from fewest to most without counting first, then count to check their guess.

Assessment

• Formative (observation): When a learner finishes counting, do they state the last number as the total?
• Self: Ask the learner to count one collection twice and tell whether their two answers matched.

Resources

• Clements, D. H., & Sarama, J. (2014). Learning and Teaching Early Math: The Learning Trajectories Approach (2nd ed.). Routledge. (Cardinality — the last counting word names the quantity.)

Home connection

At home, find two or three small collections (beans, spoons, toys). Count each one, say “how many,” then count again to check. Ask a grown-up to hide a few things so you can count and say how many.